Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/test/geo_transformations.cpp b/test/geo_transformations.cpp
new file mode 100644
index 0000000..5477657
--- /dev/null
+++ b/test/geo_transformations.cpp
@@ -0,0 +1,521 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2008-2009 Gael Guennebaud <gael.guennebaud@inria.fr>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include "main.h"
+#include <Eigen/Geometry>
+#include <Eigen/LU>
+#include <Eigen/SVD>
+
+template<typename Scalar, int Mode, int Options> void non_projective_only()
+{
+ /* this test covers the following files:
+ Cross.h Quaternion.h, Transform.cpp
+ */
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Quaternion<Scalar> Quaternionx;
+ typedef AngleAxis<Scalar> AngleAxisx;
+ typedef Transform<Scalar,3,Mode,Options> Transform3;
+ typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
+ typedef Translation<Scalar,3> Translation3;
+
+ Vector3 v0 = Vector3::Random(),
+ v1 = Vector3::Random();
+
+ Transform3 t0, t1, t2;
+
+ Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+
+ Quaternionx q1, q2;
+
+ q1 = AngleAxisx(a, v0.normalized());
+
+ t0 = Transform3::Identity();
+ VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+
+ t0.linear() = q1.toRotationMatrix();
+
+ v0 << 50, 2, 1;
+ t0.scale(v0);
+
+ VERIFY_IS_APPROX( (t0 * Vector3(1,0,0)).template head<3>().norm(), v0.x());
+
+ t0.setIdentity();
+ t1.setIdentity();
+ v1 << 1, 2, 3;
+ t0.linear() = q1.toRotationMatrix();
+ t0.pretranslate(v0);
+ t0.scale(v1);
+ t1.linear() = q1.conjugate().toRotationMatrix();
+ t1.prescale(v1.cwiseInverse());
+ t1.translate(-v0);
+
+ VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
+
+ t1.fromPositionOrientationScale(v0, q1, v1);
+ VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
+ VERIFY_IS_APPROX(t1*v1, t0*v1);
+
+ // translation * vector
+ t0.setIdentity();
+ t0.translate(v0);
+ VERIFY_IS_APPROX((t0 * v1).template head<3>(), Translation3(v0) * v1);
+
+ // AlignedScaling * vector
+ t0.setIdentity();
+ t0.scale(v0);
+ VERIFY_IS_APPROX((t0 * v1).template head<3>(), AlignedScaling3(v0) * v1);
+}
+
+template<typename Scalar, int Mode, int Options> void transformations()
+{
+ /* this test covers the following files:
+ Cross.h Quaternion.h, Transform.cpp
+ */
+ using std::cos;
+ using std::abs;
+ typedef Matrix<Scalar,3,3> Matrix3;
+ typedef Matrix<Scalar,4,4> Matrix4;
+ typedef Matrix<Scalar,2,1> Vector2;
+ typedef Matrix<Scalar,3,1> Vector3;
+ typedef Matrix<Scalar,4,1> Vector4;
+ typedef Quaternion<Scalar> Quaternionx;
+ typedef AngleAxis<Scalar> AngleAxisx;
+ typedef Transform<Scalar,2,Mode,Options> Transform2;
+ typedef Transform<Scalar,3,Mode,Options> Transform3;
+ typedef typename Transform3::MatrixType MatrixType;
+ typedef DiagonalMatrix<Scalar,3> AlignedScaling3;
+ typedef Translation<Scalar,2> Translation2;
+ typedef Translation<Scalar,3> Translation3;
+
+ Vector3 v0 = Vector3::Random(),
+ v1 = Vector3::Random();
+ Matrix3 matrot1, m;
+
+ Scalar a = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+ Scalar s0 = internal::random<Scalar>(),
+ s1 = internal::random<Scalar>();
+
+ while(v0.norm() < test_precision<Scalar>()) v0 = Vector3::Random();
+ while(v1.norm() < test_precision<Scalar>()) v1 = Vector3::Random();
+
+
+ VERIFY_IS_APPROX(v0, AngleAxisx(a, v0.normalized()) * v0);
+ VERIFY_IS_APPROX(-v0, AngleAxisx(Scalar(M_PI), v0.unitOrthogonal()) * v0);
+ if(abs(cos(a)) > test_precision<Scalar>())
+ {
+ VERIFY_IS_APPROX(cos(a)*v0.squaredNorm(), v0.dot(AngleAxisx(a, v0.unitOrthogonal()) * v0));
+ }
+ m = AngleAxisx(a, v0.normalized()).toRotationMatrix().adjoint();
+ VERIFY_IS_APPROX(Matrix3::Identity(), m * AngleAxisx(a, v0.normalized()));
+ VERIFY_IS_APPROX(Matrix3::Identity(), AngleAxisx(a, v0.normalized()) * m);
+
+ Quaternionx q1, q2;
+ q1 = AngleAxisx(a, v0.normalized());
+ q2 = AngleAxisx(a, v1.normalized());
+
+ // rotation matrix conversion
+ matrot1 = AngleAxisx(Scalar(0.1), Vector3::UnitX())
+ * AngleAxisx(Scalar(0.2), Vector3::UnitY())
+ * AngleAxisx(Scalar(0.3), Vector3::UnitZ());
+ VERIFY_IS_APPROX(matrot1 * v1,
+ AngleAxisx(Scalar(0.1), Vector3(1,0,0)).toRotationMatrix()
+ * (AngleAxisx(Scalar(0.2), Vector3(0,1,0)).toRotationMatrix()
+ * (AngleAxisx(Scalar(0.3), Vector3(0,0,1)).toRotationMatrix() * v1)));
+
+ // angle-axis conversion
+ AngleAxisx aa = AngleAxisx(q1);
+ VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
+
+ if(abs(aa.angle()) > NumTraits<Scalar>::dummy_precision())
+ {
+ VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );
+ }
+
+ aa.fromRotationMatrix(aa.toRotationMatrix());
+ VERIFY_IS_APPROX(q1 * v1, Quaternionx(aa) * v1);
+ if(abs(aa.angle()) > NumTraits<Scalar>::dummy_precision())
+ {
+ VERIFY( !(q1 * v1).isApprox(Quaternionx(AngleAxisx(aa.angle()*2,aa.axis())) * v1) );
+ }
+
+ // AngleAxis
+ VERIFY_IS_APPROX(AngleAxisx(a,v1.normalized()).toRotationMatrix(),
+ Quaternionx(AngleAxisx(a,v1.normalized())).toRotationMatrix());
+
+ AngleAxisx aa1;
+ m = q1.toRotationMatrix();
+ aa1 = m;
+ VERIFY_IS_APPROX(AngleAxisx(m).toRotationMatrix(),
+ Quaternionx(m).toRotationMatrix());
+
+ // Transform
+ // TODO complete the tests !
+ a = 0;
+ while (abs(a)<Scalar(0.1))
+ a = internal::random<Scalar>(-Scalar(0.4)*Scalar(M_PI), Scalar(0.4)*Scalar(M_PI));
+ q1 = AngleAxisx(a, v0.normalized());
+ Transform3 t0, t1, t2;
+
+ // first test setIdentity() and Identity()
+ t0.setIdentity();
+ VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+ t0.matrix().setZero();
+ t0 = Transform3::Identity();
+ VERIFY_IS_APPROX(t0.matrix(), Transform3::MatrixType::Identity());
+
+ t0.setIdentity();
+ t1.setIdentity();
+ v1 << 1, 2, 3;
+ t0.linear() = q1.toRotationMatrix();
+ t0.pretranslate(v0);
+ t0.scale(v1);
+ t1.linear() = q1.conjugate().toRotationMatrix();
+ t1.prescale(v1.cwiseInverse());
+ t1.translate(-v0);
+
+ VERIFY((t0 * t1).matrix().isIdentity(test_precision<Scalar>()));
+
+ t1.fromPositionOrientationScale(v0, q1, v1);
+ VERIFY_IS_APPROX(t1.matrix(), t0.matrix());
+
+ t0.setIdentity(); t0.scale(v0).rotate(q1.toRotationMatrix());
+ t1.setIdentity(); t1.scale(v0).rotate(q1);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0.setIdentity(); t0.scale(v0).rotate(AngleAxisx(q1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ VERIFY_IS_APPROX(t0.scale(a).matrix(), t1.scale(Vector3::Constant(a)).matrix());
+ VERIFY_IS_APPROX(t0.prescale(a).matrix(), t1.prescale(Vector3::Constant(a)).matrix());
+
+ // More transform constructors, operator=, operator*=
+
+ Matrix3 mat3 = Matrix3::Random();
+ Matrix4 mat4;
+ mat4 << mat3 , Vector3::Zero() , Vector4::Zero().transpose();
+ Transform3 tmat3(mat3), tmat4(mat4);
+ if(Mode!=int(AffineCompact))
+ tmat4.matrix()(3,3) = Scalar(1);
+ VERIFY_IS_APPROX(tmat3.matrix(), tmat4.matrix());
+
+ Scalar a3 = internal::random<Scalar>(-Scalar(M_PI), Scalar(M_PI));
+ Vector3 v3 = Vector3::Random().normalized();
+ AngleAxisx aa3(a3, v3);
+ Transform3 t3(aa3);
+ Transform3 t4;
+ t4 = aa3;
+ VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+ t4.rotate(AngleAxisx(-a3,v3));
+ VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
+ t4 *= aa3;
+ VERIFY_IS_APPROX(t3.matrix(), t4.matrix());
+
+ v3 = Vector3::Random();
+ Translation3 tv3(v3);
+ Transform3 t5(tv3);
+ t4 = tv3;
+ VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+ t4.translate(-v3);
+ VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
+ t4 *= tv3;
+ VERIFY_IS_APPROX(t5.matrix(), t4.matrix());
+
+ AlignedScaling3 sv3(v3);
+ Transform3 t6(sv3);
+ t4 = sv3;
+ VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+ t4.scale(v3.cwiseInverse());
+ VERIFY_IS_APPROX(t4.matrix(), MatrixType::Identity());
+ t4 *= sv3;
+ VERIFY_IS_APPROX(t6.matrix(), t4.matrix());
+
+ // matrix * transform
+ VERIFY_IS_APPROX((t3.matrix()*t4).matrix(), (t3*t4).matrix());
+
+ // chained Transform product
+ VERIFY_IS_APPROX(((t3*t4)*t5).matrix(), (t3*(t4*t5)).matrix());
+
+ // check that Transform product doesn't have aliasing problems
+ t5 = t4;
+ t5 = t5*t5;
+ VERIFY_IS_APPROX(t5, t4*t4);
+
+ // 2D transformation
+ Transform2 t20, t21;
+ Vector2 v20 = Vector2::Random();
+ Vector2 v21 = Vector2::Random();
+ for (int k=0; k<2; ++k)
+ if (abs(v21[k])<Scalar(1e-3)) v21[k] = Scalar(1e-3);
+ t21.setIdentity();
+ t21.linear() = Rotation2D<Scalar>(a).toRotationMatrix();
+ VERIFY_IS_APPROX(t20.fromPositionOrientationScale(v20,a,v21).matrix(),
+ t21.pretranslate(v20).scale(v21).matrix());
+
+ t21.setIdentity();
+ t21.linear() = Rotation2D<Scalar>(-a).toRotationMatrix();
+ VERIFY( (t20.fromPositionOrientationScale(v20,a,v21)
+ * (t21.prescale(v21.cwiseInverse()).translate(-v20))).matrix().isIdentity(test_precision<Scalar>()) );
+
+ // Transform - new API
+ // 3D
+ t0.setIdentity();
+ t0.rotate(q1).scale(v0).translate(v0);
+ // mat * aligned scaling and mat * translation
+ t1 = (Matrix3(q1) * AlignedScaling3(v0)) * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t1 = (Matrix3(q1) * Eigen::Scaling(v0)) * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t1 = (q1 * Eigen::Scaling(v0)) * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // mat * transformation and aligned scaling * translation
+ t1 = Matrix3(q1) * (AlignedScaling3(v0) * Translation3(v0));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+
+ t0.setIdentity();
+ t0.scale(s0).translate(v0);
+ t1 = Eigen::Scaling(s0) * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t0.prescale(s0);
+ t1 = Eigen::Scaling(s0) * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0 = t3;
+ t0.scale(s0);
+ t1 = t3 * Eigen::Scaling(s0,s0,s0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t0.prescale(s0);
+ t1 = Eigen::Scaling(s0,s0,s0) * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0 = t3;
+ t0.scale(s0);
+ t1 = t3 * Eigen::Scaling(s0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ t0.prescale(s0);
+ t1 = Eigen::Scaling(s0) * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0.setIdentity();
+ t0.prerotate(q1).prescale(v0).pretranslate(v0);
+ // translation * aligned scaling and transformation * mat
+ t1 = (Translation3(v0) * AlignedScaling3(v0)) * Transform3(q1);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // scaling * mat and translation * mat
+ t1 = Translation3(v0) * (AlignedScaling3(v0) * Transform3(q1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ t0.setIdentity();
+ t0.scale(v0).translate(v0).rotate(q1);
+ // translation * mat and aligned scaling * transformation
+ t1 = AlignedScaling3(v0) * (Translation3(v0) * Transform3(q1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // transformation * aligned scaling
+ t0.scale(v0);
+ t1 *= AlignedScaling3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // transformation * translation
+ t0.translate(v0);
+ t1 = t1 * Translation3(v0);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+ // translation * transformation
+ t0.pretranslate(v0);
+ t1 = Translation3(v0) * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // transform * quaternion
+ t0.rotate(q1);
+ t1 = t1 * q1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // translation * quaternion
+ t0.translate(v1).rotate(q1);
+ t1 = t1 * (Translation3(v1) * q1);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // aligned scaling * quaternion
+ t0.scale(v1).rotate(q1);
+ t1 = t1 * (AlignedScaling3(v1) * q1);
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // quaternion * transform
+ t0.prerotate(q1);
+ t1 = q1 * t1;
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // quaternion * translation
+ t0.rotate(q1).translate(v1);
+ t1 = t1 * (q1 * Translation3(v1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // quaternion * aligned scaling
+ t0.rotate(q1).scale(v1);
+ t1 = t1 * (q1 * AlignedScaling3(v1));
+ VERIFY_IS_APPROX(t0.matrix(), t1.matrix());
+
+ // test transform inversion
+ t0.setIdentity();
+ t0.translate(v0);
+ do {
+ t0.linear().setRandom();
+ } while(t0.linear().jacobiSvd().singularValues()(2)<test_precision<Scalar>());
+ Matrix4 t044 = Matrix4::Zero();
+ t044(3,3) = 1;
+ t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
+ VERIFY_IS_APPROX(t0.inverse(Affine).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
+ t0.setIdentity();
+ t0.translate(v0).rotate(q1);
+ t044 = Matrix4::Zero();
+ t044(3,3) = 1;
+ t044.block(0,0,t0.matrix().rows(),4) = t0.matrix();
+ VERIFY_IS_APPROX(t0.inverse(Isometry).matrix(), t044.inverse().block(0,0,t0.matrix().rows(),4));
+
+ Matrix3 mat_rotation, mat_scaling;
+ t0.setIdentity();
+ t0.translate(v0).rotate(q1).scale(v1);
+ t0.computeRotationScaling(&mat_rotation, &mat_scaling);
+ VERIFY_IS_APPROX(t0.linear(), mat_rotation * mat_scaling);
+ VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+ VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+ t0.computeScalingRotation(&mat_scaling, &mat_rotation);
+ VERIFY_IS_APPROX(t0.linear(), mat_scaling * mat_rotation);
+ VERIFY_IS_APPROX(mat_rotation*mat_rotation.adjoint(), Matrix3::Identity());
+ VERIFY_IS_APPROX(mat_rotation.determinant(), Scalar(1));
+
+ // test casting
+ Transform<float,3,Mode> t1f = t1.template cast<float>();
+ VERIFY_IS_APPROX(t1f.template cast<Scalar>(),t1);
+ Transform<double,3,Mode> t1d = t1.template cast<double>();
+ VERIFY_IS_APPROX(t1d.template cast<Scalar>(),t1);
+
+ Translation3 tr1(v0);
+ Translation<float,3> tr1f = tr1.template cast<float>();
+ VERIFY_IS_APPROX(tr1f.template cast<Scalar>(),tr1);
+ Translation<double,3> tr1d = tr1.template cast<double>();
+ VERIFY_IS_APPROX(tr1d.template cast<Scalar>(),tr1);
+
+ AngleAxis<float> aa1f = aa1.template cast<float>();
+ VERIFY_IS_APPROX(aa1f.template cast<Scalar>(),aa1);
+ AngleAxis<double> aa1d = aa1.template cast<double>();
+ VERIFY_IS_APPROX(aa1d.template cast<Scalar>(),aa1);
+
+ Rotation2D<Scalar> r2d1(internal::random<Scalar>());
+ Rotation2D<float> r2d1f = r2d1.template cast<float>();
+ VERIFY_IS_APPROX(r2d1f.template cast<Scalar>(),r2d1);
+ Rotation2D<double> r2d1d = r2d1.template cast<double>();
+ VERIFY_IS_APPROX(r2d1d.template cast<Scalar>(),r2d1);
+
+ t20 = Translation2(v20) * (Rotation2D<Scalar>(s0) * Eigen::Scaling(s0));
+ t21 = Translation2(v20) * Rotation2D<Scalar>(s0) * Eigen::Scaling(s0);
+ VERIFY_IS_APPROX(t20,t21);
+
+ Rotation2D<Scalar> R0(s0), R1(s1);
+ t20 = Translation2(v20) * (R0 * Eigen::Scaling(s0));
+ t21 = Translation2(v20) * R0 * Eigen::Scaling(s0);
+ VERIFY_IS_APPROX(t20,t21);
+
+ t20 = Translation2(v20) * (R0 * R0.inverse() * Eigen::Scaling(s0));
+ t21 = Translation2(v20) * Eigen::Scaling(s0);
+ VERIFY_IS_APPROX(t20,t21);
+
+ VERIFY_IS_APPROX(s0, (R0.slerp(0, R1)).angle());
+ VERIFY_IS_APPROX(s1, (R0.slerp(1, R1)).angle());
+ VERIFY_IS_APPROX(s0, (R0.slerp(0.5, R0)).angle());
+ VERIFY_IS_APPROX(Scalar(0), (R0.slerp(0.5, R0.inverse())).angle());
+
+ // check basic features
+ {
+ Rotation2D<Scalar> r1; // default ctor
+ r1 = Rotation2D<Scalar>(s0); // copy assignment
+ VERIFY_IS_APPROX(r1.angle(),s0);
+ Rotation2D<Scalar> r2(r1); // copy ctor
+ VERIFY_IS_APPROX(r2.angle(),s0);
+ }
+}
+
+template<typename Scalar> void transform_alignment()
+{
+ typedef Transform<Scalar,3,Projective,AutoAlign> Projective3a;
+ typedef Transform<Scalar,3,Projective,DontAlign> Projective3u;
+
+ EIGEN_ALIGN16 Scalar array1[16];
+ EIGEN_ALIGN16 Scalar array2[16];
+ EIGEN_ALIGN16 Scalar array3[16+1];
+ Scalar* array3u = array3+1;
+
+ Projective3a *p1 = ::new(reinterpret_cast<void*>(array1)) Projective3a;
+ Projective3u *p2 = ::new(reinterpret_cast<void*>(array2)) Projective3u;
+ Projective3u *p3 = ::new(reinterpret_cast<void*>(array3u)) Projective3u;
+
+ p1->matrix().setRandom();
+ *p2 = *p1;
+ *p3 = *p1;
+
+ VERIFY_IS_APPROX(p1->matrix(), p2->matrix());
+ VERIFY_IS_APPROX(p1->matrix(), p3->matrix());
+
+ VERIFY_IS_APPROX( (*p1) * (*p1), (*p2)*(*p3));
+
+ #if defined(EIGEN_VECTORIZE) && EIGEN_ALIGN_STATICALLY
+ if(internal::packet_traits<Scalar>::Vectorizable)
+ VERIFY_RAISES_ASSERT((::new(reinterpret_cast<void*>(array3u)) Projective3a));
+ #endif
+}
+
+template<typename Scalar, int Dim, int Options> void transform_products()
+{
+ typedef Matrix<Scalar,Dim+1,Dim+1> Mat;
+ typedef Transform<Scalar,Dim,Projective,Options> Proj;
+ typedef Transform<Scalar,Dim,Affine,Options> Aff;
+ typedef Transform<Scalar,Dim,AffineCompact,Options> AffC;
+
+ Proj p; p.matrix().setRandom();
+ Aff a; a.linear().setRandom(); a.translation().setRandom();
+ AffC ac = a;
+
+ Mat p_m(p.matrix()), a_m(a.matrix());
+
+ VERIFY_IS_APPROX((p*p).matrix(), p_m*p_m);
+ VERIFY_IS_APPROX((a*a).matrix(), a_m*a_m);
+ VERIFY_IS_APPROX((p*a).matrix(), p_m*a_m);
+ VERIFY_IS_APPROX((a*p).matrix(), a_m*p_m);
+ VERIFY_IS_APPROX((ac*a).matrix(), a_m*a_m);
+ VERIFY_IS_APPROX((a*ac).matrix(), a_m*a_m);
+ VERIFY_IS_APPROX((p*ac).matrix(), p_m*a_m);
+ VERIFY_IS_APPROX((ac*p).matrix(), a_m*p_m);
+}
+
+void test_geo_transformations()
+{
+ for(int i = 0; i < g_repeat; i++) {
+ CALL_SUBTEST_1(( transformations<double,Affine,AutoAlign>() ));
+ CALL_SUBTEST_1(( non_projective_only<double,Affine,AutoAlign>() ));
+
+ CALL_SUBTEST_2(( transformations<float,AffineCompact,AutoAlign>() ));
+ CALL_SUBTEST_2(( non_projective_only<float,AffineCompact,AutoAlign>() ));
+ CALL_SUBTEST_2(( transform_alignment<float>() ));
+
+ CALL_SUBTEST_3(( transformations<double,Projective,AutoAlign>() ));
+ CALL_SUBTEST_3(( transformations<double,Projective,DontAlign>() ));
+ CALL_SUBTEST_3(( transform_alignment<double>() ));
+
+ CALL_SUBTEST_4(( transformations<float,Affine,RowMajor|AutoAlign>() ));
+ CALL_SUBTEST_4(( non_projective_only<float,Affine,RowMajor>() ));
+
+ CALL_SUBTEST_5(( transformations<double,AffineCompact,RowMajor|AutoAlign>() ));
+ CALL_SUBTEST_5(( non_projective_only<double,AffineCompact,RowMajor>() ));
+
+ CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|AutoAlign>() ));
+ CALL_SUBTEST_6(( transformations<double,Projective,RowMajor|DontAlign>() ));
+
+
+ CALL_SUBTEST_7(( transform_products<double,3,RowMajor|AutoAlign>() ));
+ CALL_SUBTEST_7(( transform_products<float,2,AutoAlign>() ));
+ }
+}